INDEX
action, 115, 163, 519
activator, 175
adjoint, 448, 726
bilinear form, 322
of elliptic operator, 322
admissible states, 633
Airy’s equation, 4, 178
almost everywhere (a.e.), 733
almost separably valued function, 737
amplitude and phase, 219
analyticity, 238–245
of harmonic functions, 31
of solutions to heat equation, 62
power series, 241–245
antigradient flux function, 657
a priori estimates, 541
Arzela–Ascoli compactness criterion,
291, 479, 582, 721
asymptotics, 156, 211–233
averages, 702
acklund transformation, 696
backwards uniqueness
heat equation, 63
Banach space, 257, 264, 722
Barenblatt–Kompaneetz–Zeldovich
solution, 186
barrier, 369
basis
of eigenfunctions, 170, 357, 377, 383,
386, 388, 411, 413, 414, 531
orthonormal, 724
beam equation, 4, 450
Bernoulli’s law, 209
Bessel potential, 192
biharmonic equation, 368
bilinear form, 316
estimates for, 319–321
time-dependent, 375, 401, 426
bistable equation, 180
blow-up
conservation law, 641
nonlinear heat equation, 550, 551
nonlinear wave equation, 676,
688–693
porous medium equation, 171
reaction diffusion equation, 540
Bochner’s Theorem, 737
bootstrap argument, 489
boundary, 712
analytic, 712
Ck,
712
normal to, 713
straightening, 102, 236, 240, 339, 345,
713
boundary-value problem
eigenvalue problem, 356
homogenization of, 230
Laplace’s equation, 40
nonlinear boundary conditions, 524
nonlinear eigenvalue problem, 491
nonlinear Poisson equation, 545, 557
Poisson’s equation, 27, 41
quasilinear elliptic equation, 529, 543
second-order elliptic equation, 313,
316
745
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